The Alonso Theorem

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

Quod Erat Demonstrandum

Well, X-Alo < 0 with X being Hamilton, was about 0 with X being Trulli, and now starts to tend towards 0 with Piquet. Given what Kovalainen is doing currently against Hamilton, it is not too hard neither to guess that KOV-ALOBut when X is Fisichella being nowhere near his standard level, then you are right.

Well, X-Alo < 0 with X being Hamilton, was about 0 with X being Trulli, and now starts to tend towards 0 with Piquet. Given what Kovalainen is doing currently against Hamilton, it is not too hard neither to guess that KOV-ALOBut when X is Fisichella being nowhere near his standard level, then you are right.

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

Quod Erat Demonstrandum

Practical advise you might want to follow :

It is better to have people think you are a fool rather than to open your mouth and erase all doubts

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

Originally posted by tormave But at least this one is bashing - with style! My ignore list is already longer than the pre-season testing thread, but this one made me smile. Lighten up, dude

I never could see the point in the ignore list. Is it really such an afront to read something with which you disagree, or just think is nonsense? It is possible to ignore people without sticking your fingers in your ears and singing.

Well, X-Alo < 0 with X being Hamilton, was about 0 with X being Trulli, and now starts to tend towards 0 with Piquet. Given what Kovalainen is doing currently against Hamilton, it is not too hard neither to guess that KOV-ALOBut when X is Fisichella being nowhere near his standard level, then you are right.

you fell into his trap very nicely, dear Verkiler:

- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.

Your statement rather points to the fact that Hamilton indeed profited from Alonso developing his car. Now, with Alonso not developing his car anymore (he and Heikki have to develop now independently) the McLaren is falling behind. On the contrary, Renault starts catching up. And this is indeed seen in Piquet catching up.

Jamelo did not point to Alonso the driver but Alonso the developer in his theorem...

Originally posted by Josta I never could see the point in the ignore list. Is it really such an afront to read something with which you disagree, or just think is nonsense? It is possible to ignore people without sticking your fingers in your ears and singing.

Sorry for the off-topic response:

When there is a topic you are really interested in but 90% of bandwidth is taken by a group of fanboys typically debating something completely different, an ignore list gives you a view to the on-topic discussion that is actually possible to follow. When time is the scarce resource, ignore lists as well as spam filters are a good tool to get rid of posts that have no added value. I almost gave up this forum, but now it's mostly OK as I ignore all the angry teenagers whenever I spot them the first time.

When there is a topic you are really interested in but 90% of bandwidth is taken by a group of fanboys typically debating something completely different, an ignore list gives you a view to the on-topic discussion that is actually possible to follow. When time is the scarce resource, ignore lists as well as spam filters are a good tool to get rid of posts that have no added value. I almost gave up this forum, but now it's mostly OK as I ignore all the angry teenagers whenever I spot them the first time.

That actually makes a lot of sense now.

I have always shied away from using the ignore list since I could see no reason for it's being, just show that I simply did not understand the tool.

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s. Quod Erat Demonstrandum

I thought that ALO got beaten in t=2008-1 by driver X (- 5 years F1 experience - 2WDC) in that same identical car

When there is a topic you are really interested in but 90% of bandwidth is taken by a group of fanboys typically debating something completely different, an ignore list gives you a view to the on-topic discussion that is actually possible to follow. When time is the scarce resource, ignore lists as well as spam filters are a good tool to get rid of posts that have no added value. I almost gave up this forum, but now it's mostly OK as I ignore all the angry teenagers whenever I spot them the first time.

I disagree, largely because I find the angry teenagers amusing. I like reading the antithesis to what I believe, often because I know that I can make them look stupid with simple logic. Each to their own though .

- Take a random selection of F1 car, F1 driver (say driver "X") and track.- Take another combination of these three elements with identical car, same track and Fernando Alonso.- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.- Take a random sample of n laptimes from each.

As n tends to infinity, the difference in the average laptimes converges stochastically to 0.6s, i.e. tends to X - ALO = +0.6s.

Quod Erat Demonstrandum

So what type of convergence is this? convergence in probability, convergence in L_2, convergence in distribution, almost sure convergence?

Originally posted by MOOT So what type of convergence is this? convergence in probability, convergence in L_2, convergence in distribution, almost sure convergence?

It's a series, and I think he meant uniform convergence in z, where z is a complex Alonso personality variable. Uniform convergence is achieved for a disc of any radius that does not contain the Hamilton point.

Originally posted by MOOTSo what type of convergence is this? convergence in probability, convergence in L_2, convergence in distribution, almost sure convergence?

Stochastic convergence and convergence in probability are the same thing. Please try harder than just googling "convergence" next time.

Originally posted by aditya-now you fell into his trap very nicely, dear Verkiler:

- Allow both drivers to independently setup and develop the cars for an identical period of at least 4 months.

Your statement rather points to the fact that Hamilton indeed profited from Alonso developing his car. Now, with Alonso not developing his car anymore (he and Heikki have to develop now independently) the McLaren is falling behind. On the contrary, Renault starts catching up. And this is indeed seen in Piquet catching up.

Jamelo did not point to Alonso the driver but Alonso the developer in his theorem...

Good intro for dummies, but The Theorem is very "compact" and there's a lot more than that in it. Bear in mind that it is not impossible that a random driver is as good as Alonso in terms of ability to develop/setup a car...yet the convergence holds for any driver.

The implication is that developing and driving skills are not independent variables, there is a negative correlation. Therefore the better a driver X is developing a car, the slower he will be in terms of raw speed. This has also been proven in a different paper by a team of neurologists and it's related to the effects of ageing and driving experience in these two variables.

The Theorem proves that Alonso is the exception to that rule, hence the assymptotic result relative to any other driver. He's someone special, perhaps not from this world...but I don't want to digress.

According to the paper published in the International Journal of Mathematical Motorsports:

-Let Kd be a measure of the raw speed of a driver X in a 1-10 scale.-Let Ks be a measure of the set-up/developing ability of a driver X in a 1-10 scale.

-The sum of this two variables is always 10, i.e. Kd + Ks = 10, for any driver X. Kd and Ks are therefore negatively and perfectly correlated. The higer Kd is, the lower Ks will be and vice versa.-The sum of this variables for driver Fernando Alonso has to be exactly twice as much, i.e. 20, so Kd = Ks = 10, in order to explain the convergence.

So, although unlikely, a driver can be as good as Alonso in terms of either driving or developing, but not both. However hard he tries, it the conditions of the theorem are met, he will be 3/5 sec slower in the long run.

Last year, Hamilton and Alonso were teammates, as you probably know. The condition of independent development is therefore violated and we shouldn't expect a convergence to 0.6 necessarily. If we assume their raw speed was similar, it means Hamilton's driving is a 10 and his developing skills are zero. So this season he's in trouble. If we think Hamilton was faster, then Alonso was impeded necessarily, as beating Alonso in terms of raw speed throughtout a whole season is a mathematical impossibility.

Fisichella on the other hand was significantly slower than Alonso driving the same car, therefore his developing skills must be quite good, perhaps a 10. So with both drivers being perfect developers it was only natural that Renault got a great car in 2005 and 2006.

Stochastic convergence and convergence in probability are the same thing. Please try harder than just googling "convergence" next time.

Good intro for dummies, but The Theorem is very "compact" and there's a lot more than that in it. Bear in mind that it is not impossible that a random driver is as good as Alonso in terms of ability to develop/setup a car...yet the convergence holds for any driver.

The implication is that developing and driving skills are not independent variables, there is a negative correlation. Therefore the better a driver X is developing a car, the slower he will be in terms of raw speed. This has also been proven in a different paper by a team of neurologists and it's related to the effects of ageing and driving experience in these two variables.

The Theorem proves that Alonso is the exception to that rule, hence the assymptotic result relative to any other driver. He's someone special, perhaps not from this world...but I don't want to digress.

According to the paper published in the International Journal of Mathematical Motorsports:

-Let Kd be a measure of the raw speed of a driver X in a 1-10 scale.-Let Ks be a measure of the set-up/developing ability of a driver X in a 1-10 scale.

-The sum of this two variables is always 10, i.e. Kd + Ks = 10, for any driver X. Kd and Ks are therefore negatively and perfectly correlated. The higer Kd is, the lower Ks will be and vice versa.-The sum of this variables for driver Fernando Alonso has to be exactly twice as much, i.e. 20, so Kd = Ks = 10, in order to explain the convergence.

So, although unlikely, a driver can be as good as Alonso in terms of either driving or developing, but not both. However hard he tries, it the conditions of the theorem are met, he will be 3/5 sec slower in the long run.

Last year, Hamilton and Alonso were teammates, as you probably know. The condition of independent development is therefore violated and we shouldn't expect a convergence to 0.6 necessarily. If we assume their raw speed was similar, it means Hamilton's driving is a 10 and his developing skills are zero. So this season he's in trouble. If we think Hamilton was faster, then Alonso was impeded necessarily, as beating Alonso in terms of raw speed throughtout a whole season is a mathematical impossibility.

Fisichella on the other hand was significantly slower than Alonso driving the same car, therefore his developing skills must be quite good, perhaps a 10. So with both drivers being perfect developers it was only natural that Renault got a great car in 2005 and 2006.

Originally posted by Jamelon Good intro for dummies, but The Theorem is very "compact" and there's a lot more than that in it. Bear in mind that it is not impossible that a random driver is as good as Alonso in terms of ability to develop/setup a car...yet the convergence holds for any driver.

Stochastic convergence and convergence in probability are the same thing. Please try harder than just googling "convergence" next time.

Stocastic convergence just means convergence of random variables. There are different modes of convergence for random variables. I have a Masters in Mathematics so I know what I am talking about. At least think before you act like a smart ass next time, kiddo.http://www.ukimageho.../a9ce6b88c7.jpg

Well, according to Pat Symonds, Renault's improvement is a mere 3/10ths thus far. So I guess either Alonso's been slacking or we haven't stretched n far enough yet.

There isn't a temporal scale in this theorem so far. That could mean we need to wait another four races or another two months for the extra 0.3s or perhaps the improvement is logarithmic and take considerably longer?

Originally posted by Buttoneer There isn't a temporal scale in this theorem so far. That could mean we need to wait another four races or another two months for the extra 0.3s or perhaps the improvement is logarithmic and take considerably longer?

Or it might be that OP is talking about of his ass and that the random variables never converge, which is most likely the case.

If Renault didn't win in Barcelona is because Alonso is a very well educated driver and it's a lack of good manners winning in your own home. You have to leave the guests to win the race at home as a proof ofhospitality.

Originally posted by Josta I disagree, largely because I find the angry teenagers amusing. I like reading the antithesis to what I believe, often because I know that I can make them look stupid with simple logic. Each to their own though .

I don't know if this really is a thread that can have an off-topic discussion, but apologies anyway as there are no greek letters in this reply.

To each his own, I guess. My problem with you and other good folks who subscribe to this logic is that ignore list farmers such as myself either have to read these pointless posts quoted on your responses, or ignore you too. The other problem is that you are are really proving these people stupid to 95% of the readers, who knew it anyway. To these 5% dimwits themselves big words like "antithesis" and logic that goes against what they know in their hearts just doesn't compute.

So Josta, are you a part of the solution or a part of the problem? No need to reply, by the way... (ploink)